Measurement of Renyi entropies in multiparticle production a DO-LIST II
UL-484标准解读
• HB, HBF, and HF-1 materials may be used in the room air handling section of the unit only if all ignition sources in this section are completely enclosed in or isolated by metal or 5V material.
• b) With unit controls set for maximum cooling and maximum fan speed, switch S1 is to be closed to energize the unit. Within 5 seconds, leakage current is to be measured using both positions of switch S2. Following this and using both positions of switch S2, manual switching devices are to be operated as quickly as possible through all cooling modes, but not in the ²off²position, to determine the maximum leakage current condition.
生命用什么单位计量 写英文作文
**Measuring Life: In What Units?**Life is an intricate and multifaceted phenomenon that transcends simple quantification. While we often measure various aspects of life in tangible units—such as time, money, or achievements—the essence of life itself resists straightforward measurement. This essay explores different ways we might conceptualize and measure life, despite its inherent complexity.**Time: The Universal Measure**The most universally accepted unit for measuring life is time. From birth to death, our lives are measured in seconds, minutes, hours, days, and years. This chronological approach helps us structure our lives, set goals, and track our progress. However, time alone cannot capture the quality of our experiences or the depth of our emotions.**Health: The Physical Dimension**Health is another critical aspect often used to gauge the quality of life. Metrics such as physical fitness, mental well-being, and medical indicators provide insights into how well one is living. While these measures offer valuable information about our physical state, they don't fully encompass the richness of human experience, such as joy, fulfillment, or spiritual growth.**Economic and Social Metrics: Success and Wealth**Economic factors like income, wealth, and social status are frequently used to measure success and quality of life. These units can reflect one's standard of living and opportunities available, but they do not capture the complete picture of a person's satisfaction or happiness. Wealth and success are relative and subjective, often failing to account for personal values and inner contentment.**Personal Fulfillment: Subjective Experience**Personal fulfillment and happiness are highly subjective and vary from person to person. These dimensions of life are harder to quantify but are crucial to understanding the richness of human experience. Metrics such as life satisfaction surveys, emotional well-being indices, and personal achievement records attempt to gauge this subjective aspect, though they still fall short of fully capturing the complexity of individual lives.**Legacy and Impact: Long-Term Measures**Legacy and impact are often considered when evaluating the significance of a life. The contributions one makes to society, the relationships built, and the influence left behind can be seen as a measure of a life well-lived. While these measures reflect how one is remembered and the difference made in the world, they are retrospective and can be difficult to assess while one is still living.**Conclusion: A Multifaceted Approach**In conclusion, while we may use various units to measure aspects of life—such as time, health, economic status, and personal fulfillment—no single metric can fully capture the essence of what it means to live. Life is a rich tapestry of experiences, emotions, and achievements, andits value often defies quantification. Ultimately, the true measure of life may lie in our ability to find meaning and purpose in our unique journey, appreciating the interplay of different dimensions that make up our existence.。
FPS3Chap1Measurement
Chapter One: Measurement
Determine the number of significant figures in measurements. Distinguish accuracy, precision, and resolution. Compare data sets to determine if they are significantly different.
1.1 The meter stick
Each centimeter is divided into ten smaller units, called millimeters.
What is the length in cm?
Chapter One: Measurement
1.1 Measurements
In 1960, the Metric System was revised and simplified, and a new name was adopted— International System of Units.
1.1 International System of Measurement (SI)
Ex. There are ? cm in 1 ft? 30.48 cm = 1 ft Make a conversion factor from equivalent
4. Solution:
中文版Utrecht工作投入量表(UWES)的信效度检验
中文版Utrecht工作投入量表（ＵＷＥＳ）的信效度检验张轶文，甘怡群（北京大学心理学系，北京１００８７１）【摘要】目的：引入Ｓｃｈａｕｆｅｌｉ等编制的Ｕｔｒｅｃｈｔ工作投入量表（ＵＷＥＳ），检验其在中学教师群体中应用的信度和效度。
方法：使用ＵＷＥＳ中译本，对４７名中学教师进行初测，删去２个鉴别度过低的项目。
使用中文版Ｕｔｒｅｃｈｔ工作投入量表、ＳＦ－３６健康调查量表、ＣＯＰＥ应对量表和中学教师工作特征问卷对２７７名中学教师进行正式测量，检验各项信、效度指标。
结果：验证性因素分析结果验证了工作投入的三因素模型，各分量表内部一致性信度良好。
教师的工作投入与总体健康状况、应对策略、工作特征等效标之间存在预期的相关。
结论：修订后的中文版ＵＷＥＳ信、效度较高，可为国内相关研究所采用。
【关键词】工作投入；Ｕｔｒｅｃｈｔ工作投入量表（ＵＷＥＳ）；信度；效度中图分类号：Ｒ３９５．１文献标识码：Ａ文章编号：１００５－３６１１（２００５）０３－０２６８－０３ＴｈｅＣｈｉｎｅｓｅＶｅｒｓｉｏｎｏｆＵｔｒｅｃｈｔＷｏｒｋＥｎｇａｇｅｍｅｎｔＳｃａｌｅ：ＡｎＥｘａｍｉｎａｔｉｏｎｏｆＲｅｌｉａｂｉｌｉｔｙａｎｄＶａｌｉｄｉｔｙＺＨＡＮＧＹｉ－ｗｅｎ，ＧＡＮＹｉ－ｑｕｎＰｓｙｃｈｏｌｏｇｙＤｅｐａｒｔｍｅｎｔｏｆＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１００８７１，Ｃｈｉｎａ【Ａｂｓｔｒａｃｔ】Ｏｂｊｅｃｔｉｖｅ：ＴｏｉｎｔｒｏｄｕｃｅｔｈｅＵｔｒｅｃｈｔＷｏｒｋＥｎｇａｇｅｍｅｎｔＳｃａｌｅ（ＵＷＥＳ）ｄｅｖｅｌｏｐｅｄｂｙＳｃｈａｕｆｅｌｉｅｔａｌ，ａｎｄｔｏｅｘａｍｉｎｅｉｔｓｒｅｌｉａｂｉｌｉｔｙａｎｄｖａｌｉｄｉｔｙｉｎＣｈｉｎｅｓｅｍｉｄｄｌｅｓｃｈｏｏｌｔｅａｃｈｅｒｓ．Ｍｅｔｈｏｄｓ：Ｆｉｒｓｔ，４７ＣｈｉｎｅｓｅＭｉｄｄｌｅＳｃｈｏｏｌｔｅａｃｈｅｒｓｗｅｒｅｐｒｅｔｅｓｔｂｙｔｈｅｔｒａｎｓｌａｔｉｏｎｖｅｒｓｉｏｎｏｆＵＷＥＳ．Ｔｗｏｉｔｅｍｓｗｉｔｈｕｎｓａｔｉｓｆａｃｔｏｒｙｄｉｓｃｒｉｍｉｎａｔｉｏｎｉｎｄｅｘｗｅｒｅｄｅｌｅｔｅｄ．Ｓｅｃｏｎｄ，２７７ＣｈｉｎｅｓｅＭｉｄｄｌｅＳｃｈｏｏｌｔｅａｃｈｅｒｓｃｏｍｐｌｅｔｅｄａｂａｔｔｅｒｙｏｆｓｔｒｕｃｔｕｒｅｄｑｕｅｓｔｉｏｎｎａｉｒｅｓ，ｉｎｃｌｕｄｉｎｇｔｈｅＣｈｉｎｅｓｅｖｅｒｓｉｏｎｏｆＵＷＥＳ，ＳＦ－３６ＨｅａｌｔｈＳｕｒｖｅｙ，ＣＯＰＥａｎｄｔｈｅＪｏｂＣｈａｒａｃｔｅｒｉｓｔｉｃｓＱｕｅｓｔｉｏｎｎａｉｒｅｏｆｔｈｅＭｉｄｄｌｅＳｃｈｏｏｌｔｅａｃｈｅｒｓ．ＲｅｌｉａｂｉｌｉｔｙａｎｄｖａｌｉｄｉｔｙｏｆｔｈｅＣｈｉｎｅｓｅＵＷＥＳｗｅｒｅａｎａｌｙｚｅｄ．Ｒｅｓｕｌｔｓ：ＲｅｓｕｌｔｓｏｆｔｈｅＣｏｎｆｉｒｍａｔｏｒｙＦａｃｔｏｒＡｎａｌｙｓｉｓｃｏｎｆｉｒｍｅｄｔｈｅｈｙ－ｐｏｔｈｅｓｉｚｅｄｔｈｒｅｅ－ｆａｃｔｏｒｍｏｄｅｌｏｆｗｏｒｋｅｎｇａｇｅｍｅｎｔ，ｃｏｎｓｉｓｔｉｎｇｏｆＶｉｇｏｒ，ＤｅｄｉｃａｔｉｏｎａｎｄＡｂｓｏｒｐｔｉｏｎ．Ａｌｌｏｆｔｈｅｔｈｒｅｅｓｕｂ－ｓｃａｌｅｓｓｈｏｗｅｄａｃｃｅｐｔａｂｌｅｉｎｔｅｒｎａｌｃｏｎｓｉｓｔｅｎｃｉｅｓ．Ｗｏｒｋｅｎｇａｇｅｍｅｎｔａｎｄｉｔｓｓｕｂ－ｃｏｎｃｅｐｔｉｏｎｓｓｈｏｗｅｄｃｏｍｐｌｉｃａｔｅｄｒｅｌａｔｉｏｎ－ｓｈｉｐｓｗｉｔｈｔｈｅｇｅｎｅｒａｌｈｅａｌｔｈ，ｃｏｐｉｎｇｓｔｒａｔｅｇｉｅｓａｎｄｊｏｂｃｈａｒａｃｔｅｒｉｓｔｉｃｓ，ｗｈｉｃｈａｒｅｃｏｎｓｉｓｔｅｎｔｔｏｏｕｒｅｘｐｅｃｔａｔｉｏｎ．Ｃｏｎｃｌｕ－ｓｉｏｎ：ＴｈｅＣｈｉｎｅｓｅｖｅｒｓｉｏｎｏｆＵＷＥＳｉｓｒｅｌｉａｂｌｅａｎｄｖａｌｉｄｆｏｒａｐｐｌｉｃａｔｉｏｎｉｎＣｈｉｎａ．【Ｋｅｙｗｏｒｄｓ】Ｗｏｒｋｅｎｇａｇｅｍｅｎｔ；ＵｔｒｅｃｈｔＷｏｒｋＥｎｇａｇｅｍｅｎｔＳｃａｌｅ（ＵＷＥＳ）；Ｒｅｌｉａｂｉｌｉｔｙ；Ｖａｌｉｄｉｔｙ积极心理学主张，与心理问题和疾病的诊断与治疗、缺陷的修复等相比，发扬乐观、投入、创造力等积极品质能够更有效地促进个体发展和成长，提高工作和生活满意度，改善社会氛围［１］。
测绘专业术语
测量专业术语中英文对照及解析发布时间：2010-04-14 16:24 来自：测量meas uremen t以确定量值为目的的操作。
静态测量s tatic meas urement对测量期间其值可认为是恒定的量的测量。
注：“静态”一词适用于被测量，不适用于测量方法。
动态测量d ynamic meas ur eme nt对[变]量的瞬时值或随时间的变化值的测量。
注：“动态”一词适用于被测量，不适合于测量方法。
测量原理p rinc ip le o f meas urement测量方法的科学基础。
例如：应用于电压测量的约瑟夫森效应。
测量方法metho d o f meas ureme nt根据给定的原理，在实施测量中所涉及的理论运算和实际操作的方法。
测量步骤meas ureme nt p ro c ed ure根据给定的方法，在实施测量中所涉及的理论运算和实际操作的步骤。
被测量meas urand，meas ured q uant ity，q uant it y to b e meas ured受到测量的量。
被测变量meas ured var iab le受到测量的变量。
输入变量inp ut var iab le输入到仪器仪表的变量。
输出变量o utp ut variab le由仪器仪表输出的变量。
被测值meas ured valud在规定条件的瞬间，相当于由测量装置获得的信息，并以数值和测量单位表示的量值。
[被测量的]变换值trans fo rmed [o f a meas urand]表示与被测量有函数关系的量值。
例如：压力传感器的电输出信号值。
注：变换值可以是测量系统内部的值，或者是从系统中提供的输出。
影响量inf lue nc e q uant ity不属于被测量但却影响被测值或测量仪器仪表表示值的量。
例如：环境温度、被测交流电压的频率。
信号s igna l载有由一个或几个参数表示的一个或几个变量的信息的物理变量。
测控专业英语3
译为：测量是科学、工程、建筑及其他技术，甚至日常生活的 基础。
Measurement
(1) element In general, measuring systems comprise a number of functional elements. One element is required to discriminate the measurand and sense its dimensions or frequency. This information is then transmitted throughout the system by physical signals. If the measurand is itself active, such as water flow, it may power the signal; if passive, it must trigger the signal by interaction either with an energetic probe, such as a light source or X--ray tube, or with a carrier signal. Eventually the physical signal is compared with a reference signal of known quantity that has been subdivided or multiplied to suit the range of measurement required. The reference signal is derived from measurands of known quantity by a process called calibration.
液晶弹性常数测量+相延迟方法
Measurement of the twist elastic constant by phase retardation techniqueA. Nych, M. Voronin, V. Pergamenshchik,Yu. Kolomzarov*, V. Sorokin* and V. Nazarenko1Institute of Physics, 46 Nauki ave., Kyiv, 03039, Ukraine*Institute of Semiconductor Physics, 45 Nauki ave., Kyiv, 03028, UkraineWe have extended the experimental approach, used by Yu. A. Nastyshyn et al. [J. Appl. Phys. 86, 4199 (1999)] for measuring polar anchoring strength, to measure the twist elastic constant in nematic liquid crystal. The method implies measurements of phase retardation changes in liquid crystal under the action of magnetic field. The obtained experimental data were fitted with the predictions of elastic theory. We foundK, is in good agreement with those that the value of the measured elastic constant,22described in literature.Keywords: liquid crystal, elastic constant, phase retardation.IntroductionThe elastic constants of nematic liquid crystals have attracted considerable interest for many years and for numerous researchers [1–12]. This interest largely comes from the fact that elastic constants appreciably influence important display properties such as the threshold voltage, steepness of the electro-optical characteristic and so on. The demand to fabricate low power consumption, wide operation temperature range, high 1*****************.uacontrast and fast switching time LCDs provides the rationale for the precise knowledge of elastic constant values as well as their temperature dependence. The reason why many reports are still concerned with the elastic constants is that the measurements are far from to be trivial.The elastic constants of nematic liquid crystals are usually measured by the using Freedericksz transition induced by magnetic or electric field [1–6]. The experiments concern the investigation of direct measurement of the elastic torque exerted from a nematic sample on a glass plate were performed in [7, 10]. Other methods have been also proposed in [9] and in [11]. However, the most reliable values of elastic constants have been obtained from measurement of the Freedericksz transition in thin nematic layer. In most of these experiments the magnetic or electric field is applied perpendicular to the director. The director distortion occurs when the field exceeds a threshold value, C H . By assuming the strong anchoring of the director at the interface of the nematic layer one obtains aii C K d H χπ=, where d is the thickness of layer, a χ is anisotropy of magnetic susceptibility and ii K is an elastic constant (1=i – splay, 2=i – twist, 3=i – bend). The accuracy of the described method strongly depends on the director orientation at the interface. Even small deviation of the director results in sufficient shift of the threshold field.In the current paper we suggest an experimental technique to measure the twist elastic constant from the dependence of phase retardation of liquid crystal layer on the applied magnetic field. For a certain range of directions of the applied magnetic field the phase retardation demonstrates changes monotonically with the magnetic induction. 22K is determined from a simple fit of experimental curve.ExperimentExperiments were performed for the cells with alignment induced by coating of two glass substrates with the rubbed polyimide layer. The polyimide we used, LARC-CP1, provides almost planar orientation, the deviation of the angle between the substrate and director is less than o 1 [13]. The cells were filled with the nematic liquid crystal 5CB, purchased from EM Industries and used without any additional purification, with the parameters as following: extraordinary refractive index 708.1=e n[1], ordinary refractive index 530.1=o n [1], (both at wavelength nm 8.632=λ), anisotropy of magnetic susceptibility 3112105.113m kg a −−×=χ [5]. The optical phase retardation of the liquid crystal cell was determined by the Senarmont technique (see, for example [14, 15]). Schematically this setup is shown on Fig. 1. The light source was He-Ne laser (nm 633=λ). The linear polarized light entering the sample emerges elliptically polarized. Setting the optical axis of the quarter-wave plate parallel to the polarizer transforms the elliptically polarized light passed through the cell into linear polarized light. The measurement of the azimuth of this linear polarized light using the analyzer allows for determination of the phase retardation of the sample.Results and discussionA common nematic liquid crystal is uniaxial crystal, meaning that one crystal axis is different from the other two. The single crystal axis that is unique is often called the "extraordinary" axis and its associated refractive index is labeled e n , while the other two axes are "ordinary" axes with index o n [14]. The amount of phase retardation thatmonochromatic wave acquires from traveling trough a nematic liquid crystal is related to a refractive index, n , wavelength, λ, and the path length inside the crystal, L , as nL λπ=Φ2 (1) An input beam that is normally incident on the liquid crystal layer will be resolved into ordinary and extraordinary axis components, each with a different refractive index. The beam that emerges has a phase delay difference or retardation between the axes. Applied magnetic field results in reorientation of liquid crystal molecules along the direction of the field. Since the distortion starts in the middle of the cell the resultant structure consists of twist deformation with maximum amplitude in the center of the cell and the director coincides this rubbing directions at the interfaces. However, for normal incidence the polarization of light transmitted through the liquid crystal layer is not distinguishing from that transmitted through twisted nematic layer. There is no detectable retardation, since the polarization of light follows director deformation so the polarization of emerging light always corresponds to the director orientation at the interface. The light is "ignorant" of the deformation inside liquid crystal layer. But, when the cell is tilted toward or away from the light beam, the amount of retardation depends on the degree of tilt and has an angular sensitivity to director twist.Let us consider a homogeneously aligned nematic layer placed in magnetic field as it shown in Fig. 2. Input light, that is linearly polarized, makes a certain angle β with the cell. In the initial position the rubbing direction of the nematic cell was aligned along magnetic field. Then cell was rotated on an angle α around the normal to the cell in so manner that magnetic field induce only twist deformation of the director. In this geometry the effective extraordinary refractive index, eff n , of the LC becomesγ⋅+γ⋅⋅=2222cos sin e o oe eff n n n n n , (2)where γ is the angle between the director and input light beam. γ can be determined from defined angles β and α as follow ()ϕ−α⋅β−=γsin sin cos , where ϕ is the angle between director and rubbing direction. The angular dependent phase retardation of the liquid crystal layer is expressed as ∫−∆λπ=Φ222d d eff dz n , (3)where d is the thickness of liquid crystal layer and −γ⋅+γ⋅⋅β−=∆o e o o e i i eff n n n n n n n n 222222cos sin sin . (4)The first factor, β−22sin i in n , in eq. (4) originates from the increased optical pathlength and it takes into account a light refraction at the liquid crystal/glass interface. Just after passing an isotropic glass layer, ordinary and extraordinary beams will possess a different refraction indexes and thus they will propagate separately. To simplify our calculations we assume that both beams refract together with index of refraction, that equals to isotropic refractive index of the nematic liquid crystal, ()32e o i n n n +=.In the presence of the magnetic field, the Frank free energy density corresponding to the twist deformation is given by()202222121B n ⋅µχ− ∂ϕ∂=a d z K F (5)where 22K is the twist elastic constant, a χ is the anisotropy of the magnetic susceptibility, B is the magnetic field induction [16]. The magnetic field is taken to be small so that the energetic cost of surface director deviations can be neglected. In our geometry (see figure 2) we assume that angle α between B and rubbing direction, and thus the angle between nematic director n and B , is small. In this case equation (5) can be written as follow: ()()20222212121ϕ−α−µχ− ∂ϕ∂=B z K F a d , (6)where α is the angle between magnetic field B and rubbing direction (X -axis) and angle ϕ is the angle between nematic director n and rubbing direction. Solving the eq.(6) one can obtain the relationship between the angle of director deviation and the applied magnetic field as a function of z -coordinate:()()()()−α=ϕ2cosh cosh 1,d B q z B q B z , (6) where ()22022K B B q a µχ=, . Experimental data on the field induced change of the phase retardation, ()0=Φ−Φ=∆ΦB B B , allows one to compare these experimental data with the predictionof the elastic theory, eq. (6). The both experimental and theoretically calculated dependencies ()B ∆Φ are shown in Fig. 3, where the circles correspond to experimental values and solid lines represent calculated retardation. Within the all area of experimental data the theoretical fit is good. As an adjustable parameter to numerically solve the eq. (3) and (6) we used the elastic constant 22K . The best fit of experimentaldata provides us with the value of 22K . The measurements were carried out at the temperature 25 ºC.Thus, we obtained the following value of the twist elastic constant N 1013.31222−⋅=K . The estimated value of 22K elastic constant is approximately 10 % larger from those reported in [4] and is about the same order of magnitude with those reported in [9]. However, the choice of the a χ value may influence the value of the twist elastic constant measured in the present experiment.Finally we remark that we found good agreement of 22K with the values reported in literature [4, 9]. The developed approach can be very useful to measure the twist elastic constant in pretransitional phenomena like nematic to cholesteric transition or in twisted nematic. Further experimental and theoretical work is at present being carried out in order to make a comparison on the values of 22K obtained for uniformly aligned nematic layer and for twisted nematic layer.Acknowledgment.The authors thank Oleksandr Buluy and Andrey Dobrovolskii for help in developing of experimental set up. The present work was supported by STCU under grant #2025.Reference1. Karat P.P. and Madhusudana N.V.: Elastic and optical properties of some 4´-n-alkyl-4-cyanobiphenyls. Mol. Cryst. Liq. Cryst. 36, 51 (1976).2. Karat P.P. and Madhusudana N.V.: Elasticity and orientational order in some of4´-n-alkyl-4-cyanobiphenyls: Part II. Mol. Cryst. Liq. Cryst. 40, 239 (1977).3. Karat P.P. and Madhusudana N.V.: Orientational order and elastic constants ofsome cyanobiphenyls: Part III. Mol. Cryst. Liq. Cryst. 47, 21 (1978).4. Madhusudana N.V. and Pratibha R.: Elasticity and orientational order in some ofcyanobiphenyls: Part IV. Reanalisys of the data. Mol. Cryst. Liq. Cryst. 89, 249 (1982).5. Bradshow M.J. and Raynes E.P.: The Frank constants of some nematic liquidcrystals. J. Physique, 46, 1513 (1985).6. Schad Hp., Baur G. and Meier G.: Elastic constants and diamagnetic anisotropy ofp-disubstituted phelylcyclohexanes (PCH). J. Chem Phys., 70(06), 2770 (1979). 7. Faetti S., Gatti M. and Palleschi V.: Measurements of surface elastic torques inliquid crystals: a method to measure elastic constants and anchoring energies.Revue Phys. Appl. 21, 451 (1986).8. Coles H.J. and Sefton M.S.: Pretransitional behavior of the splay and twist elasticand viscotic constants for the nematic to smectic phase transition in octyl cyanobiphenyl (8CB). Mol. Cryst. Liq. Cryst. Lett. 4(5), 123 (1987).9. Breddels P.A. and Mulkens J.C.H.: The determination of the Frank elasticconstant for twist deformation of 4-n-pentyl-4´-cyanobiphenyl (5CB) using a conoscope. Mol. Cryst. Liq. Cryst. 147, 107 (1987).10. Faetti S. and Palleschi V.: The twist elastic constant and anchoring of the nematicliquid crystal 4-n-octyl-4´-cyanobiphenyl. Liquid Crystals, 2, 261 (1987).11. Bogi A. and Faetti S.: Elastic, dielectric and optical constants of 4´-pentyl-4-cyanobiphenyl. Liquid Crystals, 28, No. 5, 729 (2001).12. Scharkowski A., Crawford G.P., Zumer S. and Doane J.W.: A method for thedermination of the elastic constant ratio K33/K11in nematic liquid crystals.J. Appl. Phys., 73(11), 7280 (1993).13. Nazarenko V.G., Clair A.K.St., Klouda R., Polak R.D., Nastyshyn Yu. andLavrentovich O.D.: Chemically imidized polyiimide as an alignment material for LCDs. Journal of the SID, XXIX, 135 (1998).14. Born M. and Wolf E.: Principle of Optics. Pergamon, Oxford, 1980.15. Nastishin Yu.A., Polak R.D., Shiyanovskii S.V., Bodnar V.H. andLavrentovich O. D.: Nematic polar anchoring strength measured by electric field techniques. J. Appl. Phys. 86, 4199 (1999).16. de Gennes P.G.: The Physics of Liquid Crystals. Clarendon Press, Oxford, 1974.Figure captionsFigure 1. Experimental setup: L – laser, P – polarizer, R – rotating sample holder and LC cell, Q – quarter-lambda plate, A – Analyzer, Ph – Photodetector. The rotating sample holder allow the LC cell to be rotated around magnetic field direction B and around perpendicular to the cell surface direction (Z -axis). Rotation around the former axis changes the incidence angle of the laser beam β, while the angle α remains the same. Rotation around the Z -axis changes only the angle α. During these rotations magnetic field direction always lies in the plane of the cell.Figure 2. Illustration for theoretical calculations. The X -axis lies along the rubbing direction of the sample. Angle ϕ is the angle between nematic director n and X -axis (director deviation from rubbing direction). Angle α is the angle between magnetic field B and X -axis. PP’ is a line in XOY plane, perpendicular to the magnetic field direction B . Angle β is an incidence angle of laser beam. Note that during rotation around magnetic field direction only the β angle is changed and direction of light propagation K always lies in P ZP ′ plane. Angle γ is the angle between nematic director n and propagation direction of laser beam.Figure 3. Phase retardation as a function of the magnetic field. Lines represent theoretical fit for N 1013.31222−⋅=K of corresponding experimental data (squares, circles and triangles). The angle between magnetic field and rubbing direction o 20=α and the incident angle of laser beam for each data set is shown on the plot. Other parameters are as follows: 708.1=e n , 530.1=o n , 50=d µm, 3112105.113m kg a −−×=χ, 8.632=λ nm.Figure 1Figure 2Figure 3。
度量方法的同义词
度量方法的同义词Measurement methods are essential in various fields to assess and quantify different variables. These methods provide a structured approach to evaluating and understanding the characteristics and behaviors of the subject under study. However, it is important to acknowledge the limitations and considerations associated with different measurement methods.度量方法在各个领域中是必不可少的，用来评估和量化不同的变量。
这些方法为评估和理解研究对象的特征和行为提供了一种结构化的方法。
然而，重要的是要承认不同度量方法所带来的局限性和考虑因素。
One of the key considerations in choosing a measurement method is the reliability and validity of the data it produces. Reliability refers to the consistency and stability of the measurement method, while validity refers to the accuracy and meaningfulness of the data collected. It is crucial to select a measurement method that can produce reliable and valid data to ensure that the findings and conclusions drawn from the data are robust and credible.在选择度量方法时的一个关键考虑因素是它所产生的数据的可靠性和有效性。
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Here D (X, Y, Z ) is the normalized distribution of positions of particle emission points in configuration space. As seen from (1) the parameter κ ≡ κx κy κz , is a regulator of the size of the bins used for discretization of the spectrum. Note that κ need not be constant through the selected momentum space. Actually it may be — generally — convenient to vary κ with the position of the bin in momentum space. For example, in case of boost invariant distribution it is reasonable to discretize with bins of equal size in rapidity. The well-known equality dKz = E (K )dy suggests to take κz = E (Kz , K⊥ )κ(0) z , (3)
1
For a recent discussion of this point, see [7].
2
3
Discretization of the spectrum
The selected region in momentum space2 should now be divided into bins. The size of the bins is — in principle — arbitrary. It turns out to be convenient to express it in the form ∆Kx ∆Ky ∆Kz = 2π l1/(l−1)
∗ †
Address: Reymonta 4, 30-059 Krakow, Poland; e-mail: bialas@.pl; Address: Radzikowskiego 152, 31-342 Krakow, Pussing a quantum approach to the same problem [3–5]. This allows to reduce the uncertainties of the classical treatment and to formulate the improvements of the method, leading to a more precise determination of Renyi entropies from data. Since the Renyi entropy gives the lower limit on the Shannon entropy [6], such measurements may provide essential information1 on the structure of the system produced in high-energy collisions [8]. In the present paper we collect the results of [3–5] in the form of a “do list”, i.e. of an explicit prescription how to perform the measurements and how to estimate the necessary corrections. We spell out explicitly the steps to be taken to implement effectively the results of [3–5]. The importance of the dependence of measurements on discretization of particle momenta and the role of (multi)particle correlations are emphasized. The paper may be considered as an extension of the previous publication with a similar title [9], but it can be read independently.
†
Abstract Recently suggested method of measuring Renyi entropies of multiparticle systems produced in high-energy collisions is presented in the form of a “do-list”, explaining explicitely how to perform the measurement and suggesting improvements in the treatment of the data.
where E (Kz , K⊥ ) is the particle energy in the considered bin (Kz and K⊥ are the central values in this bin), while κ(0) z is a constant. Although the value of the measured Renyi entropy does not depend on the choice of κ, it should be emphasized that its selection does influence the accuracy of the measurement. The number of bins cannot be too large if one wants to keep the statistical errors under control. It follows that (1) restricts the acceptable values of κ and of the size of the momentum phase-space region which one may reasonably investigate at a given statistics of the experiment.
2
Selection of the phase-space region
As the first step in the process of measurement one has to select a phase-space region in which measurements are to be performed. This of course depends on the detector acceptance as well as on the physics one wants to investigate. The region cannot be too large because for large systems the method is difficult to apply (the requirements on statistics become too demanding). With a statistics of 106 events, the region containing (on the average) ≈ 100 or less particles should be possible to investigate. A reasonable procedure seems to be to start from a small region and then increase it until the errors become unacceptable. Comment: The proposed measurement is not restricted to systems with large number of particles. It can be applied to any multiparticle system, e.g., to e+ e− annihilation, hadron–hadron collisions or peripheral nucleusnucleus collisions. It was tested for the PYTHIA MC code for pp collisions [10] and recently employed for data on hadron–hadron collisions by the NA22 collaboration [11].
arXiv:hep-ph/0607082v2 30 Oct 2006
Measurement of Renyi Entropies in Multiparticle Production: a Do-List II
A. Bialas, W. Czyz and K.Zalewski M. Smoluchowski Institute of Physics Jagellonian University, Cracow ∗ Institute of Nuclear Physics, Polish Academy of Sciences, February 2, 2008
3/2
κx κy κz , Lx Ly Lz
(1)
where l is the rank of Renyi entropy to be measured, κx , κy , κz are arbitrary 2 2 (positive) parameters, and L2 x , Ly , Lz are the mean square radii of the system in configuration space, e.g. L2 x = ¯ )2 D (X, Y, Z )dXdY dZ . (X − X (2)